PreprintCC BY 4.0arXiv
Percolation on Finite Graphs
Abstract
Lecture notes from a graduate course given by Michael Krivelevich at the School of Mathematical Sciences of Tel Aviv University in the spring semester of 2026. Topics covered include: phase transition and the giant component in G(n,p); long paths and cycles in supercritical and sparse random graphs; thresholds for connectedness and perfect matching; general model of a random subgraph of a finite graph; phase transition and the giant component in the random hypercube; polynomial diameter of the giant component; perfect matchings in the random hypercube.
Related
- Supercritical level-set percolation on finite graphs
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- Counting Minimal Vertex Cutsets and a Gap at 1 for Site Percolation on Vertex-Transitive Graphs
BibTeX
@misc{krivelevich2026percolation,
title = {{Percolation on Finite Graphs}},
author = {Michael Krivelevich},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28552},
eprint = {2609.28552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28552},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Percolation on Finite Graphs
AU - Michael Krivelevich
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28552
UR - https://arxiv.org/abs/2609.28552
AB - Lecture notes from a graduate course given by Michael Krivelevich at the School of Mathematical Sciences of Tel Aviv University in the spring semester of 2026. Topics covered include: phase transition and the giant component in G(n,p); long paths and cycles in supercritical and sparse random graphs; thresholds for connectedness and perfect matching; general model of a random subgraph of a finite graph; phase transition and the giant component in the random hypercube; polynomial diameter of the giant component; perfect matchings in the random hypercube.
ER -